Question

The interplaner distance in a crystal is 2.8 × 10^-8 m. The value of maximum wavelength which can be diffracted : - 

• A. 2.8 × 10^-8 m
• B. 5.6 × 10^-8 m
• C. 1.4 × 10^-8 m
• D. 7.6 × 10^-8 m

Answer 1

The Correct Option is B

To find the maximum wavelength that can be diffracted by a crystal with a given interplanar distance, we use Bragg's Law:

n\lambda = 2d\sin\theta

where:

• n is the order of diffraction,
• \lambda is the wavelength,
• d is the interplanar distance, and
• \theta is the angle of incidence.

For the maximum wavelength, we assume first-order diffraction (n = 1), and the sine function has its maximum value at \theta = 90^\circ, where \sin 90^\circ = 1.

So, the equation simplifies to:

\lambda = 2d

Given that d = 2.8 \times 10^{-8} \text{ m}, we substitute into the equation:

\lambda = 2 \times 2.8 \times 10^{-8} \text{ m} = 5.6 \times 10^{-8} \text{ m}

Thus, the maximum wavelength which can be diffracted is 5.6 \times 10^{-8} \text{ m}, which corresponds to the provided correct answer:

5.6 × 10^-8 m